Categories different types of flow on the basis of their critical depth (hc)? Explain their relationship with height?

Q Categories different types of flow on the basis of their critical depth (hc)? Explain their relationship with height?

b)    Answer

1)    Super-critical flow

The flow in which depth of flow is less than critical depth, and velocity of flow and slope of channel is greater than critical flow. Supercritical flow is dominated by inertial forces and behaves as rapid or unstable flow. Supercritical flow transitions to subcritical through a hydraulic jump which represents a high energy loss with erosive potential. When the actual depth is less than critical depth it is classified as supercritical.  Supercritical flow has a Froude number greater than one

2)      Sub-critical Flow

subcritical flows are controlled from downstream (e.g. reservoir). The flow in which flow depth is greater than critical depth and flow velocity and bed slope is less then critical flow.

3)    Critical flow

The flow crossponding to minimum specific energy is called critical flow. The variation of specific energy with depth at a constant discharge shows a minimum in the specific energy at a depth at which the Froude number has a value of one.

The variation of specific energy with depth at a constant discharge shows a minimum in the specific energy at a depth called critical depth at which the Froude number has a value of one. Critical depth is also the depth of maximum discharge, when the specific energy is held constant.

c)      Also state that why subcritical flow is desirable?

Answer:

 Subcritical flow is usually preferred becase, it has a feasible flow velocity and flow is smooth. therefore, there are less chances of channel bed erosion, and increase the life of channel. It also increases the  hydraulic performance of channel.

 

An oil of sp.gr. 0.7 is flowing through a pipe of diameter 300 mm at the rate of 500 litres/s. Find the head lost due to friction and power required to maintain the floor for a length of 1000 m. Take v=0.29 stokes.

 An oil of sp.gr. 0.7 is flowing through a pipe of diameter 300 mm at the rate of 500 litres/s. Find the head lost due to friction and power required to maintain the floor for a length of 1000 m. Take v=0.29 stokes.

Solution: 

Given:-

s=0.7

Diameter of pipe, d=300mm=0.3m$d=300mm=0.3m$

Discharge, Q=500lit/s=0.5m3/s$Q=500lit/s=0.5m^3/s$

Length, L=1000m$L=1000m$

Step 1: Velocity

V=Qarea$V={\displaystyle \frac{Q}{\text{area}}}$

V=0.5π4×d2=0.5×4π×0.32=7.073m/s$V={\displaystyle \frac{0.5}{{\displaystyle \frac{\pi }{4}}\times d^2}}={\displaystyle \frac{0.5\times 4}{\pi \times {0.3}^2}}=7.073m/s$

$\mathrm{<br>}$

Step2: Reynold's Number

Re=V×dv$R_e={\displaystyle \frac{V\times d}{v}}$

Re=7.073×0.30.29×10−4$R_e={\displaystyle \frac{7.073\times 0.3}{0.29\times {10}^{-4}}}$

Re=7.316×104$R_e=7.316\times {10}^4$

${\mathrm{<br>}}^{}$

Step 3: Coefficient of friction,

f=0.079R14e$f={\displaystyle \frac{0.079}{R_e^{{\displaystyle \frac{1}{4}}}}}$

f=0.079(7.316×104)14$f={\displaystyle \frac{0.079}{(7.316\times {10}^4{)}^{{\displaystyle \frac{1}{4}}}}}$

f=0.0048$f=0.0048$

$\mathrm{<br>}$

Step 4: Head Lost

hf=4×f×L×V2d×2g$hf={\displaystyle \frac{4\times f\times L\times V^2}{d\times 2g}}$

hf=4×0.0048×1000×7.07320.3×2×9.81$hf={\displaystyle \frac{4\times 0.0048\times 1000\times {7.073}^2}{0.3\times 2\times 9.81}}$

f=163.18m$f=163.18m$

$\mathrm{<br>}$

Step 5: Power required

=ρ.g.Q.hf1000$={\displaystyle \frac{\rho .g.Q.hf}{1000}}$

Density of oil, ρ=07×1000=700kg/m3$\rho =07\times 1000=700kg/m^3$

Power required =700×9.81×0.5×163181000$={\displaystyle \frac{700\times 9.81\times 0.5\times 16318}{1000}}$

Hence power required = 560.28kWa